Question: Multiply the following complex numbers: $({3+4i}) \cdot ({-3-4i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({3+4i}) \cdot ({-3-4i}) = $ $ ({3} \cdot {-3}) + ({3} \cdot {-4}i) + ({4}i \cdot {-3}) + ({4}i \cdot {-4}i) $ Then simplify the terms: $ (-9) + (-12i) + (-12i) + (-16 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -9 + (-12 - 12)i - 16i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -9 + (-12 - 12)i - (-16) $ The result is simplified: $ (-9 + 16) + (-24i) = 7-24i $